Systems and methods for parameter optimization

ABSTRACT

Methods and systems that provide one or more recommended configurations to planners using large data sets in an efficient manner. These methods and systems provide optimization of objectives using a genetic algorithm that can provide parameter recommendations that optimize one or more objectives in an efficient and timely manner. The methods and systems disclosed herein are flexible enough to satisfy diverse use cases.

CROSS-REFERENCE

This application is a continuation of U.S. application Ser. No.16/865,707, filed on May 4, 2020, which is hereby incorporated byreference.

TECHNICAL FIELD

The disclosure relates to parameter optimization of data, moreparticularly to systems and methods using genetic algorithms inparameter optimization.

BACKGROUND

Prior to analysis of large amounts of data by machine-learningalgorithms, the data must be initially configured, and must be done sointelligently in order to obtain meaningful results from themachine-learning algorithms. The data is configured by setting one ormore parameters. Often, there are too many parameters in a configurationfor a user to choose from. In addition, there may be hundreds ofthousands of different possible values for each parameter in theconfiguration. Often, the user selects the parameters (that define theconfiguration) based on personal judgement, which turns out not to bethe best choice. The user has to experiment in terms of selecting theparameters that provide an optimal configuration. This takes time and isquite inefficient.

As an example, the configuration of supply chain parameters oftenrequires decision-makers (such as administrators and planners) to chooseparameters for the configuration. It is not immediately clear todecision-makers what choices are best or what the impacts of thesechoices are, compared to other configurations.

Continuing with the supply-chain example, a planner has as a goal toreduce the amount of late demands in a supply chain. That is, theobjective (or KPI) is the amount of late demands. One possible parameterthat can be used in the calculation of late demands is the order inwhich demands are filled across the entire supply chain. This parameteris called the transaction sequence, and is a sequence of unique numbersthat defines in which order demands are fulfilled. That is, two demandscannot be filled simultaneously. The planner can initialize thetransaction sequence, and evaluate the late demands. The planner mayaccept the results, or reset the transaction sequence, and re-evaluatethe late demand to see if there is any improvement. This continues untilthere is no further improvement of the late demands. The resultingtransaction sequence provides the optimized value of the late demand.However, there can be at least 70,000 different demands in a typicalsupply chain—requiring a planner to set at about 70,000 factorialdifferent values for the demand priorities, or sequences. However, asystematic evaluation using 70,000 factorial different transactionsequences is computationally impossible to solve. This problem gets muchmore difficult when considering multiple interdependent objectives, someof which can potentially conflict with one another. An example of thiswould be to simultaneously decrease the amount of late demands whilealso minimizing the amount of unfulfilled demands.

There is a need to provide a method that optimizes objectives based onone or more parameters, in a manner that is efficient and intelligent.

BRIEF SUMMARY

The methods and systems disclosed herein address the problem of thedifficulty by planners to select a good configuration among a vastnumber of possible configurations. The planner might not have theinformation or resources required to make an educated guess and act onit. In particular, a planner would have to manually input theconfiguration, which can be prohibitively expensive given that someconfigurations have hundreds of thousands of parameters. The methods andsystems disclosed herein intelligently search through configurations andoffers a summary of the best configurations to the planner who can thenmake an informed choice.

Disclosed herein are methods and systems that provide one or morerecommended configurations to planners in an efficient manner. Thesemethods and systems provide optimization of objectives using a geneticalgorithm that can provide parameter recommendations that optimize oneor more objectives in an efficient and timely manner. The methods andsystems disclosed herein are flexible enough to satisfy diverse usecases, while also being fast enough to ensure that planners have quickaccess to the recommendations, and can thus act promptly.

The systems and methods disclosed herein can apply to any large data setwhere parameters have to be chosen to initially configure a data setgiven later to a program (for example, a machine-learning algorithm).

In one aspect, a computer-implemented method for parameter optimizationis provided, the method comprising the steps of: defining, by aparameter optimization module, one or more objectives and one orparameters; generating, by the parameter optimization module, an initialset of values of the one or parameters; evaluating, by the parameteroptimization module, a fitness function of each objective based on theset of values of the one or parameters; obtaining, by the parameteroptimization module, a Pareto Front comprising Pareto objective points,each objective point associated with the fitness function; applying, bythe parameter optimization module, a genetic algorithm to the Paretoobjective points to generate a new set of objective points; evaluating,by the parameter optimization module, a new Pareto Front based on thenew set of objective points; comparing, by the parameter optimizationmodule, a distance between successive Pareto Fronts; and iterating, bythe parameter optimization module, through successive Pareto Frontsuntil the distance is less than a threshold. In some embodiments, whenapplying the genetic algorithm, the method further comprisescalculating, by the parameter optimization module, a plurality ofcrowding distances of the Pareto objective points; and using, by theparameter optimization module, the plurality of crowding distances todetermining pairings of the Pareto objective points. In someembodiments, the method further comprises: grouping, by the parameteroptimization module, the one or more parameters as a tree structure, thetree structure comprising one or more node levels; and applying, by theparameter optimization module, the genetic algorithm recursively to eachnode level of the tree structure.

In another aspect, a system is provided for parameter optimization, thesystem comprising: a processor; and a memory storing instructions that,when executed by the processor, configure the system to: define, by aparameter optimization module, one or more objectives and one orparameters; generate, by the parameter optimization module, an initialset of values of the one or parameters; evaluate, by the parameteroptimization module, a fitness function of each objective based on theset of values of the one or parameters; obtain, by the parameteroptimization module, a Pareto Front comprising Pareto objective points,each objective point associated with the fitness function; apply, by theparameter optimization module, a genetic algorithm to the Paretoobjective points to generate a new set of objective points; evaluate, bythe parameter optimization module, a new Pareto Front based on the newset of objective points; compare, by the parameter optimization module,a distance between successive Pareto Fronts; and iterate, by theparameter optimization module, through successive Pareto Fronts untilthe distance is less than a threshold. In some embodiments, duringapplication of the genetic algorithm, the system is further configuredto: calculate, by the parameter optimization module, a plurality ofcrowding distances of the Pareto objective points; use, by the parameteroptimization module, the plurality of crowding distances to determinepairings of the Pareto objective points. In some embodiments, the systemis further configured to: group, by the parameter optimization module,the one or more parameters as a tree structure, the tree structurecomprising one or more node levels; and apply, by the parameteroptimization module, the genetic algorithm recursively to each nodelevel of the tree structure.

In another aspect, a non-transitory computer-readable storage medium isprovided, the computer-readable storage medium including instructionsthat when executed by a computer, cause the computer to: define, by aparameter optimization module, one or more objectives and one orparameters; generate, by the parameter optimization module, an initialset of values of the one or parameters; evaluate, by the parameteroptimization module, a fitness function of each objective based on theset of values of the one or parameters; obtain, by the parameteroptimization module, a Pareto Front comprising Pareto objective points,each objective point associated with the fitness function; apply, by theparameter optimization module, a genetic algorithm to the Paretoobjective points to generate a new set of objective points; evaluate, bythe parameter optimization module, a new Pareto Front based on the newset of objective points; compare, by the parameter optimization module,a distance between successive Pareto Fronts; and iterate, by theparameter optimization module, through successive Pareto Fronts untilthe distance is less than a threshold. In some embodiments, whenapplying the genetic algorithm, the computer is further configured to:calculate, by the parameter optimization module, a plurality of crowdingdistances of the Pareto objective points; and use, by the parameteroptimization module, the plurality of crowding distances to determiningpairings of the Pareto objective points. In some embodiments, thecomputer is further configured to: group, by the parameter optimizationmodule, the one or more parameters as a tree structure, the treestructure comprising one or more node levels; and apply, by theparameter optimization module, the genetic algorithm recursively to eachnode level of the tree structure.

In another aspect, a computer-implemented method is provided forparameter optimization, the method comprising the steps of: defining, bya parameter optimization module, one or more objectives and one orparameters; generating, by the parameter optimization module, a treestructure of the one or parameters, the tree structure comprising aplurality of leaf nodes and one or more node levels; generating, by theparameter optimization module, an initial population of trees;evaluating, by the parameter optimization module, a fitness function ofeach objective at each leaf node of the plurality of leaf nodes;obtaining, by the parameter optimization module, an initial Pareto Frontcomprising Pareto objective points, each objective point associated withthe fitness function; maintaining, by the parameter optimization module,a second plurality of leaf nodes associated with the initial ParetoFront; applying recursively, by the parameter optimization module, agenetic algorithm to each node level in the tree structure of the leafnodes that form the initial Pareto Front, until the initial Pareto Frontconverges to a final Pareto Front. In some embodiments, when applyingthe genetic algorithm recursively, the method further comprises:calculating, by the parameter optimization module, a plurality ofcrowding distances of the leaf nodes and a distance of each parent node;and using, by the parameter optimization module, the plurality ofcrowding distances and the distances of each parent node to determiningpairings at each node level. In some embodiments, the genetic algorithmis a Non-dominated Sorting Genetic Algorithm (NSGA-II).

In another aspect, a system comprises: a processor; and a memory storinginstructions that, when executed by the processor, configure the systemto: define, by a parameter optimization module, one or more objectivesand one or parameters; generate, by the parameter optimization module, atree structure of the one or parameters, the tree structure comprising aplurality of leaf nodes and one or more node levels; generate, by theparameter optimization module, an initial population of trees; evaluate,by the parameter optimization module, a fitness function of eachobjective at each leaf node of the plurality of leaf nodes; obtain, bythe parameter optimization module, an initial Pareto Front comprisingPareto objective points, each objective point associated with thefitness function; maintain, by the parameter optimization module, asecond plurality of leaf nodes associated with the initial Pareto Front;apply recursively, by the parameter optimization module, a geneticalgorithm to each node level in the tree structure of the leaf nodesthat form the initial Pareto Front, until the initial Pareto Frontconverges to a final Pareto Front. In some embodiments, when the geneticalgorithm is applied recursively, the system is further configured to:calculate, by the parameter optimization module, a plurality of crowdingdistances of the leaf nodes and a distance of each parent node; and use,by the parameter optimization module, the plurality of crowdingdistances and the distances of each parent node to determining pairingsat each node level. In some embodiments, the genetic algorithm is aNon-dominated Sorting Genetic Algorithm (NSGA-II).

In another aspect, a non-transitory computer-readable storage medium isprovided, the computer-readable storage medium including instructionsthat when executed by a computer, cause the computer to: define, by aparameter optimization module, one or more objectives and one orparameters; generate, by the parameter optimization module, a treestructure of the one or parameters, the tree structure comprising aplurality of leaf nodes and one or more node level; generate, by theparameter optimization module, an initial population of trees; evaluate,by the parameter optimization module, a fitness function of eachobjective at each leaf node of the plurality of leaf nodes; obtain, bythe parameter optimization module, an initial Pareto Front comprisingPareto objective points, each objective point associated with thefitness function; maintain, by the parameter optimization module, asecond plurality of leaf nodes associated with the initial Pareto Front;apply recursively, by the parameter optimization module, a geneticalgorithm to each node level in the tree structure of the leaf nodesthat form the initial Pareto Front, until the initial Pareto Frontconverges to a final Pareto Front. In some embodiments, when applyingthe genetic algorithm recursively, the computer is further configuredto: calculate, by the parameter optimization module, a plurality ofcrowding distances of the leaf nodes and a distance of each parent node;and use, by the parameter optimization module, the plurality of crowdingdistances and the distances of each parent node to determining pairingsat each node level. In some embodiments, the genetic algorithm is aNon-dominated Sorting Genetic Algorithm (NSGA-II).

The details of one or more embodiments of the subject matter of thisspecification are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

Like reference numbers and designations in the various drawings indicatelike elements.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

To easily identify the discussion of any particular element or act, themost significant digit or digits in a reference number refer to thefigure number in which that element is first introduced.

FIG. 1 illustrates a flow chart in accordance with one embodiment.

FIG. 2 illustrates a representation of successive Pareto Fronts inaccordance with one embodiment.

FIG. 3 illustrates a subroutine for generating new objective points inaccordance with one embodiment.

FIG. 4 illustrates examples of parameter tree structures in accordancewith one embodiment.

FIG. 5 illustrates a flow chart in accordance with one embodiment.

FIG. 6 illustrates a flow chart of a nested subroutine in accordancewith one embodiment.

FIG. 7 illustrates a flow chart of a nested subroutine in accordancewith one embodiment.

FIG. 8 illustrates a leaf-solver subroutine in accordance with oneembodiment.

FIG. 9 illustrates a subroutine for generating new objective points inaccordance with one embodiment.

FIG. 10 illustrates a parent node solver subroutine in accordance withone embodiment.

FIG. 11 illustrates recommended configurations in a supply chain inaccordance with one embodiment.

FIG. 12 illustrates a block diagram of a system in accordance with oneembodiment.

DETAILED DESCRIPTION

FIG. 1 illustrates a flow chart 100 in accordance with one embodiment.

Hyperparameters are set at step 104. The hyperparameters can includealgorithmic parameters that are used in the iterative process and thegenetic algorithm. In some embodiments, the hyperparameters include:

-   -   Cross over probability (0-1.0): The probability of two        individuals mating when they are paired together;    -   Mutation probability (0-1.0): The probability that an individual        is mutated. We typically set this to 100%;    -   Diversity modification higher bound (0-1.0): The most an        individual can be modified if it is crowded next to an        individual;    -   Diversity modification lower bound (0-1.0): the least an        individual can be modified if it is crowded next to an        individual. These two numbers define a function which the        crowding distance is mapped to a mutation strength;    -   Number of trees: The number of initial guesses to make and        number of individuals that should be in the Pareto Front;    -   Retry Rate: The amount of times to retry generating new        individuals when the L1 distance is under the threshold before        determining that convergence of a pareto front has occurred; and    -   Distance Threshold: The distance that is used as a minimum        threshold to determine if a Pareto Front has converged.

At step 106, a user can define one or more objectives and choose one ormore parameters that evaluate each of the objectives.

At step 108, an initial set of parameters is generated. This initial setcan be generated randomly, using techniques known in the art. Theinitialization of the parameters is equivalent to setting an initialconfiguration of the data set. The number of initial guesses is set inthe list of hyperparameters; this number is equivalent to the number oftrees.

Each objective is evaluated by a fitness function at step 110. Theargument of each fitness function are the parameters. For example, F1(p1, p2, . . . ,pN) is the fitness function of objective ‘1’ whose valuedepends on ‘N’ parameters {p1, p2, . . . pN}. F1 is evaluated for eachinitial guess of the parameters {p1, p2, . . . pN}. The same evaluationis performed for each of the remaining fitness functions. For example,if there are ‘M’ objectives, there will be ‘M’ fitness functions [F1,F2, . . . FM], with each fitness function evaluated at each of theinitial guesses of the parameters. For example, for the first initialguess of the parameters {p1 ⁽¹⁾, p2 ⁽¹⁾, . . . , pN⁽¹⁾} there is a an“objective point” defined as the set of each fitness function evaluatedat this initial guess: [F1 ⁽¹⁾, F2 ⁽¹⁾, . . . , FN⁽¹⁾]. A plurality ofinitial objective points is generated, based on the plurality of initialguesses of the parameters.

At step 112, techniques known in the art are used to retain thoseobjective points that form a Pareto Front. That is, the objective pointsthat are retained, are non-dominated by other objective points. Thoseobjective points that are dominated by one or more other objectivepoints, are pruned (or discarded). The retained objective points arealso referred to as the “Pareto Front”. An illustration of Pareto Frontsis shown in FIG. 2 .

At step 114, the objective points (and their associated parameters) aresent to a genetic algorithm to generate a new set of objective points atstep 116. In addition, one or more hyperparameters may be sent to thegenetic algorithm as required. The combined steps can form geneticalgorithm subroutine 128 that allows for variations in the way thegenetic algorithm generates a new set of objective points. This geneticalgorithm subroutine 128 is further discussed in FIG. 3 .

Non-limiting examples of genetic algorithms that may be used in thesystems and methods for parameter optimization include: Strength ParetoEvolutionary Algorithm (SPEA2), Pareto Envelope Selection Algorithm(PESA), Pareto Archived Evolution Strategy (PAES), Niched Pareto GeneticAlgorithm (NPGA), and Non-dominated Sorting Genetic Algorithm (NSGA-II).

Many of these genetic algorithms differ in their selection operator (howparings are determined) and pruning mechanisms (how Pareto Front pointsare selected). Non-limiting examples of Mating Operators include:Uniform Partially Matched (used primarily for permutations); SimulatedBinary Bounded (used primarily for decimal values); and UniformCrossover (used primarily for binary values). Non-limiting examples ofMutation Operators include: Shuffle Indexes (primarily forpermutations); Polynomial Bounded Mutation (primarily for decimalvalues); and Binary Bit Flip Mutation (primarily for binary values).

At step 118, pruning takes place to provide a new Pareto Front. That is,the new set of objective points are pruned so as to retain only thoseobjective points that are non-dominated.

At step 120, the distance (L1) between the new Pareto Front and theprevious Pareto Front is evaluated, by techniques known in the art.

At decision block 122, the distance (L1) is compared to a thresholdvalue set in the hyperparameters at step 104. If the distance is greaterthan the threshold, then step 114, step 118 and step 120 are repeateduntil convergence of the Pareto Front occurs at step 124. The objectivepoints on the converged Pareto Front are retained, and the associatedparameters for each objective point, provide a configuration for theuser. These objective points serve as recommendations for the user,which is shown in the Example below. The program ends at step 126.

FIG. 2 illustrates a representation 200 of successive Pareto Fronts inaccordance with one embodiment. In the example of FIG. 2 , there are twoobjectives. The filled circles 202 represent a previous Pareto Frontgenerated at step 112 of FIG. 1 . An example of a crowding distance 204,defined as the distance between two objective points on a Pareto Front,is shown in FIG. 2 . The hollow circles 206 represent a new ParetoFront, obtained at step 118 of FIG. 1 . The distance between theprevious and new Pareto Fronts can be calculated by techniques know inthe art. If this distance is less than a threshold hyperparameter, thenthe generation of new pareto fronts ceases (step 124 of FIG. 1 ).

FIG. 3 illustrates a genetic algorithm subroutine 128 for generating newobjective points in accordance with one embodiment. At step 302,crowding distances between objective points on the Pareto Front arecalculated (see 204 in FIG. 2 for an illustration of a crowdingdistance). A genetic algorithm receives the set of objective points onthe current Pareto Front, along with the crowding distances of eachobjective point, at step 304. At step 306, the genetic algorithm usesthe crowding distances to determine which objective points will pair forfurther manipulation. It then applies mating and mutation operators onthe pairings at step 308 and generates a new set of objective points atstep 310.

Examples of genetic algorithms include Non-dominated Sorting GeneticAlgorithm (NSGA)-II.

When the number of parameters is greater than 1, a tree structure of theparameters can be used to enhance the method shown in FIG. 1 . FIG. 4illustrates examples 400 of parameter tree structures in accordance withone embodiment.

The node with the lowest-level node (node level=1) is called the rootnode; nodes with the highest-level node (node level=number ofparameters) are called leaf nodes. Note that if there is only oneparameter, the tree structure has only one node level.

As an example, suppose there are two parameters {P1, P2}. Initialguesses of these parameters can be put into a tree structure, as shownin two-parameter tree structure 402. Here, P1=B and P2=C. There are twolevels of nodes in this tree structure, with B occupying a node level of1, and C occupying a node level of 2. The C-level nodes are referred toas “leaf nodes”, since the tree structure ends at C. The B-level node isa parent node of the C-level node, and is also the root node.

Suppose there are three initial random guesses for B={1, 2, 3} and twoinitial random guesses for C={5, 6}. That is, there are 6 initial pairsof random guesses {B, C}. These can be put into a tree structure, whereB has a common value for each value of C. As an example, thetwo-parameter tree structure 402 can represent the pairs {B=1, C=5} and{B=1, C=6}. There are a total of three tree structures that representall of the initial guesses: {B=1; C=5 and C=6}, {B=2; C=5 and C=6}, and{B=3; C=5 and C=6}.

Three-parameter tree structure 404 provides an example of threeparameters {P1, P2, P3}. Initial guesses of these parameters can be putinto a tree structure. Here, P1=A, P2=B and P3=C. There are three levelsof nodes, with A occupying a node level of 1, B occupying a node levelof 2 and C occupying a node level of 3. The C-level nodes are referredto as “leaf nodes”, since the tree structure ends at C. The B-level nodeis a parent node of the C-level node, and the A-level node is a parentof the B-level node. The A-level node is also the root node for thistree structure. For any given C-node, its parent nodes B and A arecalled its lineage.

Suppose there are 2 initial random guesses for A={2,3}, two initialrandom guesses for B={1, 2} and three initial random guesses for C={5,6, 7}. That is, there are 12 initial triplets of random guesses {A,B,C}. These can be put into a tree structure as follows: set A={2}. Thesix triplets for the tree structure are {A=2, B=1, C=5}; {A=2, B=1,C=6}; {A=2, B=1, C=7}; {A=2, B=2, C=5}; {A=2, B=2, C=6} and {A=2, B=2,C=7}. There are a total of two tree structures that represent all of theinitial triplet guesses.

While specific examples of tree structures are shown in FIG. 4 ,parameter tree structures can take on any number of children at any nodelevel.

FIG. 5 illustrates a flow chart 500 in accordance with one embodiment,that is variation of the flow chart 100 shown in FIG. 1 , in which aparameter tree structures are used to find the final Pareto Front.

As in FIG. 1 , hyperparameters are set at step 504 and at step 506, auser can define one or more objectives and choose one or more parametersthat evaluate each of the objectives. The parameters are grouped as atree structure at step 508, with the number of node levels in the treeequal to the number of parameters. Recall from the description of FIG. 4above that the node with the lowest-level node number (NL=1) is the rootnode; nodes at the highest-level node number (NL=number of parameters)are the leaf nodes.

At step 510, an initial population of trees generated. This initial setcan be generated randomly, using techniques known in the art. Theinitialization of the parameters is equivalent to setting an initialconfiguration of the data set. The number of initial guesses is set inthe list of hyperparameters; this number is equivalent to the number oftrees.

At step 512, the fitness function of each objective at each leaf node isevaluated, while at step 514, techniques known in the art are used toretain those leaf nodes that form a Pareto Front. That is, the leafnodes that are retained, are non-dominated by other leaf nodes. Thoseleaf nodes that are dominated by one or more other leaf nodes, arepruned (or discarded). The retained leaf nodes form the Pareto Front.

At step 516, for each leaf node in the parent front (at step 514), alist of parameter nodes is gathered. This information is provided to setof nested subroutines at step 518 that exploit the parameter treestructure to arrive at a converged Pareto Front. The leaf nodes of theconverged Pareto Front are retained at step 520 and provide a list ofrecommended solutions. The nested subroutines comprise a leaf-solversubroutine and a parent-node solver subroutine. These are discussedbelow. The program ends at step 522.

FIG. 6 illustrates a flow chart of nested subroutines in accordance withone embodiment where there are three parameters. At step 602, theleaf-solver subroutine is applied to the current Pareto Front generatedat step 514 in FIG. 5 to provide a converged Pareto Front, which is theninput to the parent node solver subroutine at step 604.

At step 604, the parent node level is set at 2. With reference to thethree-parameter tree structure 404 (in FIG. 4 ), the parent node solveris applied to parent parameters designated by ‘B’. The parent nodesolver subroutine ultimately provides a new Pareto Front based on a newset of leaf nodes that are generated by a new set of parent ‘B’ nodes.

The leaf node solver subroutine is applied once again at step 606 toprovide a newly converged Pareto Front. At step 608, parent node solversubroutine is applied to the converged Pareto Front that is input.However, this time, the parent node level is set to 1. With reference tothe three-parameter tree structure 404 (in FIG. 4 ), the parent nodesolver is now applied to parent parameters designated by ‘A’, therebygenerating a new set of ‘A’ nodes, and ensuing new set of ‘B’ nodes and‘C’ nodes (i.e. Leaf nodes).

The leaf node solver is applied again at step 610 for the new leafnodes, which generates a newly-converged Pareto Front, followed byre-application of the parent node solver at step 612, in which the ‘B’parent nodes are used to generate a new set of ‘C’ (i.e. leaf) nodes.The leaf node solver is applied one last time at step 614, after which aconverged Pareto front is obtained. The program ends at step 616.

A description of each of the leaf node solver subroutine and the parentnode solver subroutine are provided below.

FIG. 7 illustrates a flow chart of nested subroutines in accordance withone embodiment where there are three parameters. FIG. 7 is similar tothe nested subroutine described in FIG. 6 , except that a series ofhybrid converged Pareto Fronts are constructed.

At step 702, the leaf-solver subroutine is applied to the current ParetoFront generated at step 514 in FIG. 5 to provide a converged ParetoFront at step 704, which is then input to the parent node solversubroutine at step 706.

At step 706, the parent node level is set at 2. With reference to thethree-parameter tree structure 404 (in FIG. 4 ), the parent node solveris applied to parent parameters designated by ‘B’. The parent nodesolver subroutine ultimately provides a new Pareto Front based on a newset of leaf nodes that are generated by a new set of parent B′ nodes.

The leaf node solver subroutine is applied once again at step 708 toprovide a newly converged Pareto Front at step 710, which is compared tothe previously converged Pareto Front obtained at step 704. At step 712,a hybrid-converged Pareto Front is constructed from the two convergedPareto fronts, which is then used as input at step 714.

At step 714, parent node solver subroutine is applied to the convergedPareto Front that is input. However, this time, the parent node level isset to 1. With reference to the three-parameter tree structure 404 (inFIG. 4 ), the parent node solver is now applied to parent parametersdesignated by ‘A’, thereby generating a new set of ‘A’ nodes, andensuing new set of B′ nodes and ‘C’ nodes (i.e. Leaf nodes).

The leaf node solver is applied again at step 716 for the new leafnodes, which generates a newly-converged Pareto Front at step 718. Thisnewly converged Pareto Front obtained at step 718 is compared to thehybrid Pareto Front obtained at step 712, and a new hybrid Pareto Frontis constructed at step 720 from these two Pareto Fronts.

At step 722, the hybrid Pareto Front (obtained at step 720) is input toparent node solver, in which the B′ parent nodes are used to generate anew set of ‘C’ (i.e. leaf) nodes. The leaf node solver is applied onelast time at step 724, after which a newly converged Pareto front isobtained at step 726. A final hybrid Pareto Front is constructed at step728 from the converged Pareto Front obtained at step 726 and the hybridPareto Front at step 720. The program ends at step 730.

A description of each of the leaf node solver subroutine and the parentnode solver subroutine are provided below.

FIG. 8 illustrates a leaf-solver subroutine 800 in accordance with oneembodiment. This subroutine roughly corresponds to step 114 to step 124in FIG. 1 .

At step 802, the leaf nodes on the current Pareto Front are sent to thegenetic algorithm to generate a new set of leaf nodes at step 804, whichare then pruned to provide a new Pareto

Front at step 806. The distance between the new and previous Paretofronts are compared at step 808. If this distance is less than athreshold value (set in the hyperparameters), the Pareto Front is deemedto have converged. If not, then step 802-decision block 810 are repeateduntil convergence is obtained, at which point the leaf nodes on theconverged Pareto Front are retained at step 812.

Genetic algorithm subroutine 814 of the leaf node solver subroutine isdiscussed further with reference to FIG. 9 .

FIG. 9 illustrates a genetic algorithm subroutine 814 for generating newleaf nodes accordance with one embodiment. At step 902, crowdingdistances between leaf nodes s on the Pareto Front are calculated (see204 in FIG. 2 for an illustration of a crowding distance). A geneticalgorithm receives the set of leaf nodes on the current Pareto Front,along with the crowding distances of each leaf node, at step 904. Atstep 906, the genetic algorithm uses the crowding distances to determinewhich objective points leaf nodes will pair for further manipulation. Itthen applies mating and mutation operators on the pairings at step 908and generates a new set of leaf nodes at step 910. In some embodiments,only leaf nodes with the same lineage are eligible for mating with eachother.

Examples of genetic algorithms include Non-dominated Sorting GeneticAlgorithm (NSGA)-II.

FIG. 10 illustrates a parent node solver subroutine 1016 in accordancewith one embodiment. At step 1004, parent node solver subroutine 1016receives as input, the converged Pareto Front from leaf node solversubroutine (see FIG. 8 ).

At step 1006, the crowding distance of each leaf node is used todetermine a distance of each parent node. In some embodiments, anaverage crowding distance is used to determine a distance of each parentnode.

At step 1002, the parent node distances are sent to the geneticalgorithm which uses this information to determine suitable pairings ofthe parent nodes at step 1008. The genetic algorithm then applies matingand mutation operators on the suitable pairings of parent nodes at step1010. This generates a new set of parent nodes at step 1012, which inturn generates a new set of leaf nodes. The new leaf nodes are prunedsuch that a new Pareto Front is obtained at step 1014.

The parent node solver subroutine 1016 is used to generate a new set ofparent nodes for any node level except the leaf node level. These newparent nodes, in turn, generate new leaf nodes, and a new Pareto Front.

FIG. 11 illustrates recommended configurations 1100 in a supply chain inaccordance with one embodiment.

In FIG. 11 , there are two objectives. Namely, to increase on-timedemands 1102 while decreasing unfulfilled demands 1104. The parameterused to evaluate each objective is the demand prioritization, which isthe same as a transaction sequence discussed above. The geneticalgorithm used was NSGA-II for selection, while Uniform PartiallyMatched used for the mating operator and Shuffle Indexes used for themutation operator.

The supply chain analyzed in FIG. 11 contains in excess of 70,000different demands across the entire supply chain, resulting in 70,000factorial possible different transaction sequences. The system andmethod generate three recommendations—one which maximizes on-timedemands 1102; one which minimizes unfulfilled demands 1104, while thethird provides a balanced recommendation between both objectives. Theseare all evaluated according to business needs. While the results shownin FIG. 11 weigh each objective equally during the calculation, thesystems and methods can weigh each objective in terms of its individualimportance.

In recommendation 1106, the on-time demands 1102 is maximized through anoptimization of the demand prioritization. In this recommended scenario,the optimized parameter increases the on-time demands 1102 by 12% priorto application of the algorithm. In this example, the base value ofon-time demands 1102 is 19,523 demands. However, the drawback is thatthese same optimized parameters increase the unfulfilled demands 1104 by1%, compared to pre-parameter optimization. In this example, the basevalue of unfulfilled demands 1104 is 102 demands. Overall though, theon-time quantity 1108, defined as the amount of units delivered on timeto their destination, increases by 142M units.

In recommendation 1110, the unfulfilled demands 1104 is maximizedthrough an optimization of the demand prioritization. In thisrecommended scenario, the optimized parameters decrease the unfulfilleddemands 1104 by 18%—which is a far better situation for this objectivethan in recommendation 1106. Furthermore, in this scenario, the on-timedemands 1102 increase by 11%, slightly less than the 12% increase shownin recommendation 1106.

Here, the on-time quantity 1108 increases by 137M units, which is not ashigh as the 142M unit increase shown in recommendation 1106.

Finally, in recommendation 1112, the demand prioritization is optimizedby finding a balance between the on-time demands 1102 and theunfulfilled demands 1104—rather than trying to prioritize one over theother. In this recommended scenario, the optimized parameters decreasethe unfulfilled demands 1104 by 8%—which is a far better situation forthis objective than in recommendation 1106, but less so thanrecommendation 1110. Furthermore, in this scenario, the on-time demands1102 increase by 12%, equal to the increase shown in recommendation1106, and slightly better than the 11% increase shown in recommendation1110. Here, the on-time quantity 1108 increases by 141M units, which isslightly less than the 142M unit increase shown in recommendation 1106,but higher than the 137M unit increase of recommendation 1110.

Once the recommendations are provided to the planner, s/he is free tochoose one. For example, a planner may opt to choose recommendation1110, if the main goal is to minimize the unfulfilled demands 1104—eventhough its on-time quantity goes up by 137M units, which is less thanthat of other recommendations. Or, the planner may choose recommendation1112, since the balanced approach provides for on-time demands 1102 andunfulfilled demands 1104 that are acceptable, while providing an on-timequantity 1108 increase of 141M units.

In general, the number of recommendations is set at the outset of themethod. It is possible that the final number of recommendations obtainedmay be less than the number of recommendations set at the outset. In thecase of the example shown in FIG. 11 , eight recommendations were setfor the analysis. While eight recommendations were obtained, only threeare shown.

The recommendations shown, were all based on an excess of 70,000 demandsover three years of an international supply chain. The processing timeto arrive at the three different scenarios was only 40 minutes. It isimpossible for a modern computer to find a single solution out of themassive number of 10¹⁰⁰ ⁰⁰⁰ different parameter configurations in theconventional approach, as it would take longer than the age of theuniverse to compute. The systems and methods disclosed herein providerecommended configurations quickly and efficiently, and allow ourplanners to act promptly on these recommendations.

FIG. 12 illustrates a block diagram of system 1200 in accordance withone embodiment.

System 1200 includes a system server 1202 and client server 1214. Systemserver 1202 can include a memory 1206, a disk 1208, a processor 1204 anda parameter optimization module 1210. While one processor 1204 is shown,the system server 1202 can comprise one or more processors. In someembodiments, memory 1206can be volatile memory, compared with disk 1208which can be non-volatile memory. In some embodiments, system server1202 can communicate with client server 1214 via network 1212.

System 1200 can also include additional features and/or functionality.For example, system 1200 can also include additional storage (removableand/or non-removable) including, but not limited to, magnetic or opticaldisks or tape. Such additional storage is illustrated in FIG. 12 bymemory 1206 and disk 1208. Storage media can include volatile andnonvolatile, removable and non-removable media implemented in any methodor technology for storage of information such as computer-readableinstructions, data structures, program modules or other data. Memory1206 and disk 1208 are examples of non-transitory computer-readablestorage media. Non-transitory computer-readable media also includes, butis not limited to, Random Access Memory (RAM), Read-Only Memory (ROM),Electrically Erasable Programmable Read-Only Memory (EEPROM), flashmemory and/or other memory technology, Compact Disc Read-Only Memory(CD-ROM), digital versatile discs (DVD), and/or other optical storage,magnetic cassettes, magnetic tape, magnetic disk storage or othermagnetic storage devices, and/or any other medium which can be used tostore the desired information and which can be accessed by system 200.Any such non-transitory computer-readable storage media can be part ofsystem 1200.

Communication between system server 1202 and client server 1214 vianetwork 1212 can be over various network types. Non-limiting examplenetwork types can include Fibre Channel, small computer system interface(SCSI), Bluetooth, Ethernet, Infrared Data Association (IrDA), Localarea networks (LAN), Wireless Local area networks (WLAN), wide areanetworks (WAN) such as the Internet, serial, and universal serial bus(USB). Generally, communication between various components of system 200may take place over hard-wired, cellular, Wi-Fi or Bluetooth networkedcomponents or the like. In some embodiments, one or more electronicdevices of system 200 may include cloud-based features, such ascloud-based memory storage.

Client server 1214 can provide a variety of raw data from the user foruse by the parameter optimization module 1210. In addition, theobjectives may be computed at client server 1214. In some embodiments,the raw data includes, but is not limited to: point of sales data thatindicates the sales record of all of the client's products at everylocation; the inventory history of all of the client's products at everylocation; promotional campaign details for all products at alllocations, and events that are important/relevant for sales of aclient's product at every location.

Parameter optimization module 1210 includes all of the resource wherethe operations (e.g. (initialization, mutation, mating, etc.) of thevarious routines and subroutines occur. The genetic algorithms andassociated operators are also stored within the parameter optimizationmodule 1210.

Using network 1212, system server 1202 can retrieve data from clientserver 1214. The retrieved data can be saved in memory 1206 or disk1208. In some cases, system server 1202 can also comprise a web server,and can format resources into a format suitable to be displayed on a webbrowser.

Although the algorithms described above including those with referenceto the foregoing flow charts have been described separately, it shouldbe understood that any two or more of the algorithms disclosed hereincan be combined in any combination. Any of the methods, modules,algorithms, implementations, or procedures described herein can includemachine-readable instructions for execution by: (a) a processor, (b) acontroller, and/or (c) any other suitable processing device. Anyalgorithm, software, or method disclosed herein can be embodied insoftware stored on a non-transitory tangible medium such as, forexample, a flash memory, a CD-ROM, a floppy disk, a hard drive, adigital versatile disk (DVD), or other memory devices, but persons ofordinary skill in the art will readily appreciate that the entirealgorithm and/or parts thereof could alternatively be executed by adevice other than a controller and/or embodied in firmware or dedicatedhardware in a well-known manner (e.g., it may be implemented by anapplication specific integrated circuit (ASIC), a programmable logicdevice (PLD), a field programmable logic device (FPLD), discrete logic,etc.). Further, although specific algorithms are described withreference to flowcharts depicted herein, persons of ordinary skill inthe art will readily appreciate that many other methods of implementingthe example machine readable instructions may alternatively be used. Forexample, the order of execution of the blocks may be changed, and/orsome of the blocks described may be changed, eliminated, or combined.

It should be noted that the algorithms illustrated and discussed hereinas having various modules which perform particular functions andinteract with one another. It should be understood that these modulesare merely segregated based on their function for the sake ofdescription and represent computer hardware and/or executable softwarecode which is stored on a computer-readable medium for execution onappropriate computing hardware. The various functions of the differentmodules and units can be combined or segregated as hardware and/orsoftware stored on a non-transitory computer-readable medium as above asmodules in any manner and can be used separately or in combination.

Particular embodiments of the subject matter have been described. Otherembodiments are within the scope of the following claims. For example,the actions recited in the claims can be performed in a different orderand still achieve desirable results. As one example, the processesdepicted in the accompanying figures do not necessarily require theparticular order shown, or sequential order, to achieve desirableresults. In certain implementations, multitasking and parallelprocessing may be advantageous.

What is claimed is:
 1. A computer-implemented method for parameteroptimization, the method comprising the steps of: defining, by aparameter optimization module, one or more objectives and one or moreparameters; generating, by the parameter optimization module, a treestructure of the one or more parameters, the tree structure comprising aplurality of leaf nodes and one or more node levels; generating, by theparameter optimization module, an initial population of trees;evaluating, by the parameter optimization module, a fitness function ofeach objective at each leaf node of the plurality of leaf nodes;obtaining, by the parameter optimization module, an initial Pareto Frontcomprising Pareto objective points, each objective point associated withthe fitness function; maintaining, by the parameter optimization module,a second plurality of leaf nodes associated with the initial ParetoFront; applying recursively, by the parameter optimization module, agenetic algorithm to each node level in the tree structure of the leafnodes that form the initial Pareto Front, thereby generating one or morehybrid Pareto fronts, until the initial Pareto Front converges to afinal Pareto Front.
 2. The method of claim 1, wherein when applying thegenetic algorithm recursively, the method further comprises:calculating, by the parameter optimization module, a plurality ofcrowding distances of the leaf nodes and a distance of each parent node;and using, by the parameter optimization module, the plurality ofcrowding distances and the distances of each parent node to determiningpairings at each node level.
 3. The method of claim 1, whereingeneration of each hybrid Pareto front comprises: generating a firstconverged Pareto front by application of the genetic algorithm to afirst set of leaf nodes; and generating a second converged Pareto frontby application of the genetic algorithm to a first set of parentalnodes.
 4. The method of claim 1, wherein when applying the geneticalgorithm, the method further comprises: calculating, by the parameteroptimization module, a plurality of crowding distances of the Paretoobjective points; and using, by the parameter optimization module, theplurality of crowding distances to determining pairings of the Paretoobjective points.
 5. The method of claim 1, wherein the geneticalgorithm is a Non-dominated Sorting Genetic Algorithm (NSGA-II).
 6. Asystem comprising: a processor; and a memory storing instructions that,when executed by the processor, configure the system to: define, by aparameter optimization module, one or more objectives and one or moreparameters; generate, by the parameter optimization module, a treestructure of the one or more parameters, the tree structure comprising aplurality of leaf nodes and one or more node levels; generate, by theparameter optimization module, an initial population of trees; evaluate,by the parameter optimization module, a fitness function of eachobjective at each leaf node of the plurality of leaf nodes; obtain, bythe parameter optimization module, an initial Pareto Front comprisingPareto objective points, each objective point associated with thefitness function; maintain, by the parameter optimization module, asecond plurality of leaf nodes associated with the initial Pareto Front;apply recursively, by the parameter optimization module, a geneticalgorithm to each node level in the tree structure of the leaf nodesthat form the initial Pareto Front, thereby generating one or morehybrid Pareto fronts, until the initial Pareto Front converges to afinal Pareto Front.
 7. The system of claim 6, wherein when applying thegenetic algorithm recursively, the system is further configured to:calculate, by the parameter optimization module, a plurality of crowdingdistances of the leaf nodes and a distance of each parent node; andusing, by the parameter optimization module, the plurality of crowdingdistances and the distances of each parent node to determining pairingsat each node level.
 8. The system of claim 6, wherein when generatingeach hybrid Pareto front, the system is further configured to: generatea first converged Pareto front by application of the genetic algorithmto a first set of leaf nodes; and generate a second converged Paretofront by application of the genetic algorithm to a first set of parentalnodes.
 9. The system of claim 6, wherein when applying the geneticalgorithm, the system is further configured to: calculate, by theparameter optimization module, a plurality of crowding distances of thePareto objective points; and using, by the parameter optimizationmodule, the plurality of crowding distances to determining pairings ofthe Pareto objective points.
 10. The system of claim 6, wherein thegenetic algorithm is a Non-dominated Sorting Genetic Algorithm(NSGA-II).
 11. A non-transitory computer-readable storage medium, thecomputer-readable storage medium including instructions that whenexecuted by a computer, cause the computer to: define, by a parameteroptimization module, one or more objectives and one or more parameters;generate, by the parameter optimization module, a tree structure of theone or more parameters, the tree structure comprising a plurality ofleaf nodes and one or more node levels; generate, by the parameteroptimization module, an initial population of trees; evaluate, by theparameter optimization module, a fitness function of each objective ateach leaf node of the plurality of leaf nodes; obtain, by the parameteroptimization module, an initial Pareto Front comprising Pareto objectivepoints, each objective point associated with the fitness function;maintain, by the parameter optimization module, a second plurality ofleaf nodes associated with the initial Pareto Front; apply recursively,by the parameter optimization module, a genetic algorithm to each nodelevel in the tree structure of the leaf nodes that form the initialPareto Front, thereby generating one or more hybrid Pareto fronts, untilthe initial Pareto Front converges to a final Pareto Front.
 12. Thecomputer-readable storage medium of claim 11, wherein when applying thegenetic algorithm recursively, the instructions that when executed bythe computer, further cause the computer to: calculate, by the parameteroptimization module, a plurality of crowding distances of the leaf nodesand a distance of each parent node; and using, by the parameteroptimization module, the plurality of crowding distances and thedistances of each parent node to determining pairings at each nodelevel.
 13. The computer-readable storage medium of claim 11, whereinwhen generating each hybrid Pareto front, the instructions that whenexecuted by the computer, further cause the computer to: generate afirst converged Pareto front by application of the genetic algorithm toa first set of leaf nodes; and generate a second converged Pareto frontby application of the genetic algorithm to a first set of parentalnodes.
 14. The computer-readable storage medium of claim 11, whereinwhen applying the genetic algorithm, the instructions that when executedby the computer, further cause the computer to: calculate, by theparameter optimization module, a plurality of crowding distances of thePareto objective points; and using, by the parameter optimizationmodule, the plurality of crowding distances to determining pairings ofthe Pareto objective points.
 15. The computer-readable storage medium ofclaim 11, wherein the genetic algorithm is a Non-dominated SortingGenetic Algorithm (NSGA-II).